Theorems · Inductive type · field theory
IsTopologicalDivisionRing
(K : Type u_1) → [DivisionRing K] → [TopologicalSpace K] → Prop
A topological division ring is a division ring with a topology where all operations are continuous, including inversion.
- Defined in
- Mathlib.Topology.Algebra.Field
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- DivisionRingTopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- DivisionRingstatement · cited by 1,062
Cited by11
Results whose statement or proof uses this declaration.
- Subfield.topologicalClosurestatement and proof · cited by 5
- UniformSpace.Completion.hatInv_extendsstatement and proof · cited by 2
- Complex.uniformContinuous_ringHom_eq_id_or_conjproof · cited by 1
- Subfield.isClosed_topologicalClosurestatement and proof · cited by 1
- Subfield.le_topologicalClosurestatement and proof · cited by 1
- Subfield.topologicalClosure_minimalstatement and proof · cited by 0
- UniformSpace.Completion.mul_hatInv_cancelstatement and proof · cited by 0
- UniformSpace.Completion.coe_invstatement and proof · cited by 0
- Subfield.topologicalClosure.congr_simpstatement and proof · cited by 0
- IsTopologicalDivisionRing.casesOnstatement and proof · cited by 0
- IsTopologicalDivisionRing.recOnstatement and proof · cited by 0